Nowadays nonlinear fiber effects, such as self-phase modulation, SPM for short and cross-phase modulation, XPM for short, are the main limitation for increased transmission distance and/or higher throughput over an optical fiber link or a fiber link, respectively. The origin is that longer transmission distance and higher capacity require more optical power in the fiber in order to meet the required optical signal-to-noise ratio, OSNR for short, at the receiver end. However, at a certain power level, nonlinear fiber effects, such as SPM and XPM, convert amplitude modulation into phase modulation onto data present in the fiber. SPM occurs when amplitude modulation of a transmitted signal imposes a phase modulation onto the same signal and XPM corresponds to the case when amplitude modulation is converted to phase modulation of a signal at a different wavelength. In a dense wavelength division multiplexed communication system, DWDM system for short, XPM introduces crosstalk between adjacent wavelength channels and SPM introduces distortion within a particular DWDM channel.
FIG. 1 shows the principle of linear and nonlinear limitation of optical transmission performance according to the prior art. The OSNR limit is due to noise, fundamentally generated by amplifiers and other active components, and the nonlinear limit arises because of nonlinear distortion in the optical fiber. The dashed line in FIG. 1 indicates a typical result in a practical fiber link. In other words, FIG. 1 illustrates linear and nonlinear limitation in bit-error-ratio, BER for short, versus optical power into an optical link. At low input power, the BER becomes lower for increased optical power due to a corresponding increase in OSNR while at a certain point the BER saturates and eventually becomes worse for further increase in optical power due to fiber nonlinearities. The left part of the curve in FIG. 1 indicates the BER limitation due to OSNR only, i.e. with no impact of nonlinearities, and the right part of the curve in FIG. 1 indicates the limitation due to fiber nonlinearities. The dashed line exemplifies a typical behavior of BER versus span launch optical power for a conventional multi-span transmission link or a conventional optical link, respectively. The nonlinear limit in FIG. 1 is a fundamental limitation to further increase the reach and/or capacity of fiber optic transmission systems and thus there is currently a big effort within the fiber optic industry to find ways to push the nonlinear limit towards higher optical power levels.
Nonlinearities can to some extent be mitigated by either hardware- or software-based mitigation techniques. Hardware-based techniques include mid-span spectrum inversion that requires an optical spectrum inverter approximately in the middle of the link but has the advantage of not requiring any additional signal processing. Software-based mitigation techniques for SPM have been extensively investigated during the last few years due to the possibility to implement such techniques in a digital signal processor, DSP for short, but have so far not been used commercially due to extremely large computation complexity. The best technique used in the DSP so far is called digital back propagation, DBP for short, which tries to numerically estimate the optical field at various positions in the fiber in order to determine the impact of SPM. When the amount of phase rotation of a received symbol is estimated, this can be corrected in the received symbol and thus reduce the possibility of an erroneously detected symbol.
An alternative possibility to increase the capacity in fiber optic systems could be to utilize better optical amplifiers that add less noise to the signal and thus allow longer transmission distances or higher spectral efficiency. Today erbium-doped fiber amplifiers, EDFAs for short, are massively deployed and these have a theoretical noise figure, NF for short, of 3 dB.
The main problem with DBP is the extreme computation complexity required in the DSP that has to be performed on every received symbol. Already at around 10 Gbit/s to 100 Gbit/s per DWDM channel, the required computation complexity is not practically possible to implement in any DSP hardware available today and most likely not even within foreseeable time. All experimental results are so far performed in DSPs implemented with so-called off-line processing where a short batch of sampled data is processed in a computer using very long time and complex calculation software written in, for instance, MATLAB or C programming language. Another fundamental problem with DBP is that XPM cannot be included since that would require information about what information is present on the disturbing adjacent DWDM channels which is in general not possible since these DWDM channels are independent of each other.